(CBS NEWS) -- Senate Republicans, who spent most of the last week bemoaninga recent rules change that makes it easier for Democrats to confirm
Obama
administration appointees, will have to turn their attention this week
to the
two-year budget deal crafted by the heads of the House and Senate Budget
Committees, Rep. Paul Ryan, R-Wis., and Sen. Patty Murray, D-Wash.

But in a deviation from the usual patterns in Washington,
the bipartisan agreement may have a harder path in the Senate, where lawmakers
are typically less averse to compromise than their House counterparts.

"The struggle is still on in the United States Senate," Sen. Dick
Durbin, D-Ill., the number two Democrat in the Senate, said Sunday on CBS News' "Face
the Nation."

Durbin predicted Democrats will need "about eight"
Republicans to vote with them in favor of the deal. Because Democrats control
55 votes in the Senate (that includes two independents who usually vote with
them), that means Durbin is likely counting on a few Democratic senators voting "no" on the deal. Senate Majority
Leader Harry Reid, D-Nev., has scheduled a procedural vote on the measure for
Tuesday that will require 60 yes votes to overcome.

If Durbin's vote counting is correct, Senate leaders have a
long way to go this week. His diagnosis: a heaping helping of potential
political angst for those who vote yes.

"A handful of members of the Senate are vying for the
presidency in years to come and thinking about this vote in the context. And
others are frankly afraid of this new force, the tea party force, the Heritage
Foundation force, that is threatening seven out of the 12 Republican senators
running for re-election," Durbin said.

Indeed, many Republicans have come out against the deal,
ranging from Sen. Jeff Sessions, R-Ala., the top Republican on the Senate Budget Committee,
to lawmakers like Sen. Lindsey Graham, R-S.C., who are up for reelection in 2014, to the handful of Republicans
eyeing the White House in 2016, including Sens. Ted Cruz of Texas, Rand Paul of Kentucky
and Marco Rubio of Florida.

Sen.
John McCain, R-Ariz., is one of the only Republican senators who has
definitely said he will vote for the deal. In an appearance on "Face the
Nation," he said he supported it because it undoes some of the budget
cuts for defense spending
mandated by the sequester.

"I think it's important that we have this agreement," McCain
said. "The devastation to our national security -- ask any of our military
leaders, and I know you have -- that's being inflicted by this sequestration,
as it is, is so harmful."

A handful of other Republicans have said they will vote to end debate on the bill and move to a final vote, but
aren't sure yet whether they will be supporting it.

Outside
conservative groups came out aggressively against the deal but still found
themselves shut out when the House passed
it with a solid bipartisan majority that included more than half of the
Republican conference. Last week, House Speaker John Boehner, R-Ohio, publicly
lashed out at the groups, saying
they had "lost all credibility" and were just using Republican lawmakers and the American people.

House GOP
leaders came to the floor to voice support the deal before their members voted
last week, and Durbin said they are also reaching out to some of their Senate
colleagues to persuade them to go along.

If the deal passes both chambers, it will be significant for
Congress, which has spent years budgeting by emergency legislation rather than
normal order. But even Ryan, one of the deal's authors, admitted it's mostly a "symbolically
large agreement."

"I would love to throw a few more zeros at the end of these
numbers, but the fact that we're doing this, preventing the shutdowns, passing
bipartisan legislation. It passed the House 332-94, majority of both parties.
That's a good step in the right direction. You've got to crawl before you can
walk before you can run," he said on NBC's "Meet the Press" in a join interview
with Murray.

For her part, Murray said both parties will need to learn
how to trust each other enough to compromise. That's the only way Democrats and
Republicans have any hope at striking any more budget deals or confronting the
tough fights ahead in 2014, such as the impending debate over whether to raise the nation's debt limit.

But the deal seems to have provided some hope that is
possible. Ryan said the House Ways and Means Committee was planning to advance tax
reform legislation in the first quarter of next year, a long elusive prospect
in Washington.